In general, this pattern is found when the second adjective and the following noun are treated as one set phrase. (Compare "a kind old man" vs "a kind and old man" in English; "old man" is clearly treated as a set phrase in the former case.) In addition, くて is often avoided in lyrics or poems where people sometimes ignore formal grammar in favor of rhythm.
But this does not explain your example since this text is prose and 固い柿の実 is not a set phrase. I think this まだ modifies both 青い and 固い because a 柿 fruit gets softer as it ripens. So, in your case, I think まだ青くて固い柿の実 is better, and I don't see any good reason to prefer 青い固い here. It doesn't sound terribly bad, either, so I think you can regard this as a trivial mistake, and get moving.